Oberon has at different points been king of elves and / or fairies… both of which have been known as “fair folk”, but presumably have only diverged in definition in recent times.
Titania, in essence and position, was a creation of Shakespeare…. and in that context she is undeniably a fairy queen and not an elf…

But still. Figures that if we’re used to those two names being together, and Oberon in at least one telling is considered elven… then it makes sense for his wife to be so too.